The methods used for determining soil permeability and groundwater flow.

1. Laboratory and Indirect Methods

Permeability ($K$) can be determined using both direct testing and empirical formulas based on soil properties.
Indirect Formulas



Kozeny-Karman Equation: Used to relate permeability to the void ratio ($e$) and specific surface area. The formula is given as:



$$k=\frac{1}{k_{k}}\frac{e^{3}}{(1+e)}\frac{\gamma}{\mu}$$


Allen Hazen Formula: Typically used for clean sands.


$$K=CD_{10}^{2}$$


The constant $C$ usually ranges from 100 to 150; if not specified, $C=100$ is used.



Terzaghi Method: Another empirical approach for permeability:


$$K=200~e^{2}\times D_{10}^{2}$$



Consolidation Equation: Relates permeability to the coefficient of consolidation ($C_v$) and volume compressibility ($m_v$).

Direct Laboratory Tests

Falling Head and Constant Head Tests: These are standard laboratory procedures used primarily for saturated soils, though they can sometimes be adapted for partially saturated soils.

2. Field Methods (Pumping Tests)

Field methods are used for large areas where water is pumped out of a well to observe the aquifer's response.

Unconfined Aquifers

Dupuit Theory: Used to calculate discharge ($Q$) in unconfined conditions.



$$Q=\frac{\pi k(H^{2}-h_{w}^{2})}{2.303~log(\frac{R}{r_{w}})}$$



Thiem's Theory: Uses two observation wells to determine permeability.



$$Q=\frac{\pi k(H_{1}^{2}-H_{2}^{2})}{2.303~log(\frac{r_{1}}{r_{2}})}$$

Confined Aquifers

For confined aquifers, the thickness of the aquifer ($D$) is a critical factor.


Dupuit Theory (Confined):


$$Q=\frac{2\pi KD(H-h_{w})}{2.303~log(\frac{R}{r_{w}})}$$


Thiem's Theory (Confined):


$$Q=\frac{2\pi kD(H_{1}-H_{2})}{2.303~log(\frac{r_{1}}{r_{2}})}$$

3. Transmissibility

Transmissibility ($T$) represents the rate at which water is transmitted through a full thickness of an aquifer.



Formula: $T = KD$


Units: Typically expressed in $m^2/day$




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